Question

# Find the sum of all natural numbers between $$250$$ and $$1000$$ which are exactly divisible by $$3$$.

Solution

## Clearly the numbers between $$250$$ and $$1000$$ which are divisible by $$3$$ are $$252$$, $$255$$, $$258$$,________ $$999$$.$$\therefore T_n=999=a+(n-1)d=252+(n-1)3$$$$333=84+n-1$$$$\therefore n=333-83=250$$$$\therefore S=\dfrac{n}{2}[a+l]=(250/2)[252+999]$$$$=125\times 1251=156375$$.Mathematics

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